Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 3 - Section 3.1 - Congruent Triangles - Exercises: 6

Answer

The statment that the triangles are congruent is as follows: $$\triangle ABC\cong\triangle FED$$

Work Step by Step

Since two triangles are congruent, and $\angle CAB\cong\angle DFE$, two sides of $\triangle ABC$ that includes $\angle CAB$ are each congruent with two sides of $\triangle DEF$ that includes $\angle DFE$. That means $\overline{AB}\cong\overline{FE}$ and $\overline{AC}\cong\overline{FD}$. Therefore, $\overline{BC}\cong\overline{ED}$, since two triangles are congruent. That means, the statment that the triangles are congruent is as follows: $$\triangle ABC\cong\triangle FED$$ (Notice the order of the corresponding points. Any sides $\overline{AB}$, $\overline{AC}$ or $\overline{BC}$ must be congruent with the corresponding sides of $\triangle FED$. The angles must be congruent as well.)
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